I just want to make sure that the following assumption is equivaent to the first postulate. Consider two inertial frames S and S'. By inertial frame, is meant, a frame where all the laws of physics are valid in their simplest form. Now let an observer in S measure the velocity of S' to be 'v' towards his/her right. Now we automatically assume, that when an observer in S' measures the velocity of S, he/she will measure it to be 'v' to his/her left. How can we say that the two observers will agree on the magnitude of the velocities they measure, of the other frame, from their frame? Is this just an assumption equivalent to the first postulate of relativity which says that : Given an inertial frame S, a frame S' moving with constant velocity with respect to S, will also be inertial. According o the above postilate then, Given S is inertial, and an observer in S measures constant v as the velocity of S', this implies S' is inertial. Now we know S' is inertial and S is also inertial, so an observer in S' measuring the velocity of S would observe a constant velocity according to the first postulate. It doesn't however garauntee that this velocity's magnitude is going to be v itself.